紧致单连通流形上余维二的奇异黎曼叶状结构
微分几何
2025-12-25 v3
摘要
我们证明了，在紧致单连通黎曼-流形上，具有同胚于-环面的正则叶的余维二奇异黎曼叶状结构，由一个光滑有效的-环面作用给出。这以否定方式解决了关于单连通流形上是否存在由奇异环面构成的叶状结构的余维情形问题。
引用
@article{arxiv.1903.07191,
title = {A-Foliations of codimension two on compact simply-connected manifolds},
author = {Diego Corro},
journal= {arXiv preprint arXiv:1903.07191},
year = {2025}
}
备注
35 pages, 3 figures. Proposition 4.3 is now Theorem B in the introduction and Proposition 3.3 in the text. Corollary 4.8 appears now also as Theorem D. We added a question in page 5 of the Introduction. Section 3 of the previous version is now Section 6. Section 3.1 is now Section 6.2 and Section 3.2 is now Section 6.1. Remark 4.9 has been added